Difference operation on Boolean modifier not showing once applied
The simplest definition of Boolean with the Difference operation is that it eliminates the common region that is occupied by 2 geometries. 
 

In your project, You may notice that both the geometries share a common region.


You added the modifier to the Cylinder with Choker as the target object.
Ultimately the some the Cylinder part will get removed as the modifier is for the Cylinder, not for the Choker. But you want a hole in the Choker.So the best solution is to add the Boolean modifier to the Choker, with Difference as the operation, and the target object as the Cylinder.

However there will still be some portion remaining in the bottom.


So you have to apply the modifier and delete it in Edit Mode. But you may have to apply the first 2 modifiers to get the desired result.


Hope this helped!